A really interesting plot could be a fanfiction that explores what if Lois Lane was the one who had to mediate between Batman and Superman. She could use her journalistic skills to uncover the misunderstandings that led to their conflict and bring them together. This would add a whole new layer to the story as she tries to navigate the complex relationship between the two heroes.
One idea could be a story where Batman and Superman have to team up against a common enemy before their big fight actually happens. Maybe a powerful alien threat that forces them to realize they need each other's skills.